Question

A local cell phone store just received a shipment of 760 cell phone chargers. The manager wants to estimate the number of defective cell phone chargers in the shipment. Rather than checking every cell phone charger, the manager plans to take a simple random sample of size 76 in order to estimate the proportion of defective cell phone chargers in the shipment. If the sample proportion of defective cell phone chargers, p̂, is greater than 0.0263 (there are more than two defective cell phone chargers in the sample), the manager will file a complaint and request a new shipment.

Suppose that the true proportion of defective cell phone chargers in the shipment is approximately p = 0.01.

What is the expected value of the sample proportion?

E(p̂)=

Since the sample is to be drawn from a finite population, and since the sample is greater than/less than/equal to 5% of the population size, the finite population correction factor is not/ is needed when you calculate the standard deviation of the sampling distribution.

What is the standard deviation of the sampling distribution of the sample proportion

σp̂ =

0.01(1 – 0.01)

0.01

√[(760 – 76) / (760 – 1)]√[0.01/76]

√[(760 – 76) / (760 – 1)]√[0.01(1-0.01)/76]

0.01/√76

Answer 1

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